To determine which reaction represents beta decay, it's important to understand what beta decay is. Beta decay occurs when a neutron in an atom's nucleus transforms into a proton and an electron (beta particle), or vice versa, and the electron (or positron) is emitted from the nucleus. There are two types of beta decay: beta-minus (β-) decay and beta-plus (β+) decay.
In beta-minus decay (β-), a neutron converts into a proton, and an electron (β-) plus an anti-neutrino are emitted:
[tex]\[ n \rightarrow p + \beta^- + \overline{\nu} \][/tex]
Hence, the atomic number (number of protons, [tex]\(Z\)[/tex]) increases by 1, while the mass number (sum of protons and neutrons, [tex]\(A\)[/tex]) remains unchanged.
In the options given:
- Option A represents an alpha decay:
[tex]\[ { }_{93}^{235} Np \rightarrow{ }_{91}^{231} Pa+\alpha \][/tex]
An alpha particle ([tex]\(\alpha\)[/tex]) consists of 2 protons and 2 neutrons ([tex]\( {}_2^4 He \)[/tex]). Here, the atomic number decreases by 2, and the mass number decreases by 4.
- Option B represents a gamma decay:
[tex]\[ { }_{28}^{60} Ni \rightarrow{ }_{28}^{60} Ni + \gamma \][/tex]
Here, a gamma photon ([tex]\(\gamma\)[/tex]) is emitted, but the atomic number and mass number remain unchanged.
- Option C also represents an alpha decay:
[tex]\[ { }_{86}^{220} Rn \rightarrow{ }_{84}^{216} Po + { }_2^4 He \][/tex]
Here again, the atomic number decreases by 2, and the mass number decreases by 4.
- Option D represents a beta-minus decay:
[tex]\[ { }_{83}^{212} Bi \rightarrow{ }_{84}^{212} Po + { }_{-1}^0 e \][/tex]
In this reaction, bismuth ([tex]\( { }_{83}^{212} Bi \)[/tex]) decays into polonium ([tex]\( { }_{84}^{212} Po \)[/tex]), and a beta particle ([tex]\( { }_{-1}^0 e \)[/tex]) is emitted. The atomic number increases by 1 (83 to 84), while the mass number remains the same (212).
Therefore, the correct answer is:
D. [tex]\( { }_{83}^{212} Bi \rightarrow{ }_{84}^{212} Po + { }_{-1}^0 e \)[/tex]
